1. Field of the Invention
The present invention relates in general to signal validation systems, and more specifically to a signal validation system in the control system of a nuclear reactor; the signal validation system being capable of determining direct current (DC) drift and noise components in signal discrepancies.
2. Description of the Related Art
Reliability is an important consideration in many areas of technology, such as advanced avionic systems and the control systems of nuclear reactors. The use of redundant components, at least two, and more typically three or four components, is one technique that is used to increase reliability. The advantage of redundant components is that when a failure of one of the components is detected, the remaining component(s) which produce signals conveying the same information can still be used. Thus, system reliability becomes a function of the ability to identify and handle component failures.
In the case of signals output by sensors, several types of failures are possible, including: bias--due to D.C. drift or noise, hardover--to a maximum or minimum level; sticking--at a given level; or common mode--where more than one sensor fails in the same manner, more or less simultaneously. In the case of sensors which output positive and negative values corresponding to the maximum and minimum values of a hardover error, null failure, resulting in the output of a zero value, is also possible.
A powerful tool for identifying many types of failures while requiring relatively little variation for specific control systems, is provided by the parity-space algorithm. The parity-space algorithm was originally developed for advanced avionic systems as described in Potter and Suman, "Thresholdless Redundancy Management with Arrays of Skewed Instruments," Integrity in Electronic Flight Control Systems, NATO AGARDOGRAPH-224, 1977, pages 15-1 to 15-25 incorporated by reference herein. The application of the parity-space algorithm to control of nuclear reactors is described in a report available from the Electric Power Research Institute, Inc. as the Final Report dated Nov. 19, 1981 of NP-2110, Research Project 1541, by Deckert et al., entitled On-line Power Plant Signal Validation Technique Utilizing Parity-Space Representation and Analytic Redundancy incorporated by reference herein. As described therein, application of the parity-space algorithm to a specific system only requires determination of an error boundary for each sensor in the system.
The parity-space algorithm provides information concerning discrepancies between redundant measurements of a parameter. Rather than comparing the measurements against a reference value, the parity-space algorithm looks at the differences between the values. As a result, the number of dimensions q of a parity vector generated by the parity-space algorithm is equal to the number of measurements of a parameter minus the dimensions of the parameter. For example, according to the parity-space algorithm, l measurements of a scalar parameter produce a parity vector having q=l-1 dimensions.
One particular type of parity space has been termed "orthogonal parity space" by Potter and Suman in their article referenced above. As defined therein, orthogonal parity space has the following properties. An orthogonal parity vector p is defined according to equation (1), where V is an upper triangular matrix that transforms l measurements in an l by 1 column vector m into the parity vector p. EQU p=Vm (1)
The measurement vector m is defined according to equation (2), where x is the actual value of the parameter being measured and has n dimensions where n equals 1 if the parameter being measured is a scaler, .epsilon. is the error in each of the measurements, and H is an l by n matrix. EQU m=Hx+.epsilon. (2)
Thus, when a scalar is measured by three sensors, H is defined by equation (3). ##EQU1## In orthogonal parity space, matrix V is defined to have the properties of equation (5) where matrix K is defined as in equation (4). EQU K=(H.sup.T H).sup.-1 H.sup.T ( 4) EQU V.sup.T V=I-HK=W (5)
From equation (5) it follows that equations (6) and (7) are true. EQU VV.sup.T =KH=I (6) EQU VH=KV.sup.T =0 (7)
Given the above characteristics of matrix V, Potter and Suman have found that the elements of the matrix V are defined by equations (8)-(12). ##EQU2##
The simplest application of the parity-space algorithm in orthogonal parity space occurs when a scalar parameter (n=1) is measured by three sensors (l=3). In this case, the matrix H is defined by equation (3) and, as defined in equation (4), K=1/3[1,1,1]. Using the definition in equation (5), the elements of matrix W have the values in equation (13). ##EQU3## The formulas in equation (8)-(12) give the following results for matrix V. ##EQU4## The columns of matrix V are vectors of length .sqroot.2/3 which lie along the measurement axes in parity space. Plotting these vectors results in a positively valued measurement axis every 120.degree., as illustrated in FIG. 1.
As a result of the special properties of orthogonal parity space, several meaningful values can be found using a minimum amount of calculation when the parameter being measured is a scalar. A residual .eta..sub.j can be found for each of the measurements m.sub.j by subtracting the mean m from each measurement m.sub.j, i.e., .eta..sub.j =m.sub.j -m, where m is calculated according to equation (15). ##EQU5## The residuals can then be reordered from smallest to largest, as indicated in equation (16). EQU .eta..sub.1 .ltoreq..eta..sub.2 .ltoreq. . . . .ltoreq..eta..sub.l ( 16)
After the reordering, there is a one-to-one correspondence between the measurements m.sub.j and the residuals .eta..sub.j, but the residual .eta..sub.2, for example, is not necessarily the residual for the measurement m.sub.2. After such reordering, a projection p.sub.j of the parity vector along the measurement axis of each sensor j can be can be calculated according to equation (17). EQU P.sub.j =.sqroot.l/(l-1).multidot..eta..sub.j ( 17)
Given measurements from three sensors, for example, the parity vector 10 will be two-dimensional and thus easily depicted on a display screen 20, as illustrated in FIG. 1. In the case of such a two-dimensional parity vector 10, it is relatively easy to convert the projection p.sub.j into two-dimensional component parity vectors (the coordinates of the parity vector in the plane), or into sensor components of the parity vector in the direction of the measurement axes, using appropriate geometric and trigonometric relationships. An example of conversion will be given in the Description of the Preferred Embodiment.
Failure of any one of the sensors can be detected by analyzing the parity vector. When the sensors are assumed to have a uniform error boundary b, at least one of the sensors is in error if the inequality (18) is satisfied, where .delta..sub.a is defined by equations (19a) and (19b). ##EQU6##
In many cases, it is possible to identify which of the sensors has failed by calculating orthogonal components ##EQU7## in accordance with equation (20) for each of the sensors. ##EQU8## Since the residuals .eta..sub.j were ordered according to equation (16) above, the orthogonal component ##EQU9## will have the largest value of any of the orthogonal components. Therefore, if the orthogonal component ##EQU10## is small, i.e., the inequality in equation (21), where .delta..sub.l-1 is defined by equations (19a) and (19b), is true for j=1, then no inconsistency has been detected in the measurements supplied by the sensors and the value of the parameter measured by the sensors can be estimated as the mean m. ##EQU11## If the inequality in equation (21) is not satisfied for j=1, then the inequality is tested repeatedly for each value of j=2 through j=l. As j gets larger, the value of p.sup.2.sub.j will get smaller. If the inequality in equation (7) is satisfied for a value of j between 2 and l-1, inclusive, then the sensor which produced the inconsistency cannot be positively identified, and the best estimate for the value of the parameter measured by the sensors is m, where m is defined by equation (22). ##EQU12## If the first value of j which satisfies the inequality in equation (21) is l, then the sensor which generated the residual .eta..sub.l can be identified as having produced the inconsistent measurement and equation (22), with j=l, can be used for the best estimate m of the value of the parameter measured by the sensors.
If none of the measurements can be identified as having been inconsistent, then the above procedure is repeated, throwing out the measurement which generated the largest residual .eta..sub.l. This is equivalent to decrementing the value of l by 1 and repeating equations (15) through (22). However, if the value of l is decremented below three, i.e., only two measurements are left, without isolating an inconsistent measurement, it is impossible to isolate the inconsistent measurement using the conventional parity-space algorithm.
Assuming this does not occur, when the equation in (21) is satisfied and the value of the decremented l is at least three, then the estimate m for the value of the parameter measured by the sensors can be calculated according to equation (22). However, if the value of j which satisfies the inequality in equation (21) equals the value of the decremented l, it is necessary to compare the measurements of the excluded sensors with the measurement of the sensor having the orthogonal component ##EQU13## which satisfied equation (21) to determine whether the difference therebetween is less than the error-bound b. In other words, if the inequality in equation (23) is true for any value of k greater than the value of j and less than or equal to the original value of l, where the value of j equals the value of the decremented l, then a common mode inconsistency has occurred which the parity-space algorithm is unable to isolate. EQU .vertline.m.sub.k -m.sub.j .vertline..ltoreq.2b (23)
When a sensor is identified as having generated consecutive inconsistent measurements, for example, three times, then that sensor is identified as having failed.
As described above, although the basic parity-space algorithm is extremely powerful, it has limitations with respect to the types of failures which are detected. For example, a sensor may have a significant amount of DC drift, e.g., due to poor calibration, without having actually failed. Since the parameter-space algorithm does not distinguish between noise and DC drift contributions to inconsistent measurements, the information which could be provided by analysis of these components is not utilized.